We highlight the trends leading to the increased appeal of using hybrid multicore+GPU systems for high performance computing. We present a set of techniques that can be used to develop efficient dense linear algebra algorithms for these systems. We illustrate the main ideas with the development of a hybrid LU factorization algorithm where we split the computation over a multicore and a graphics processor, and use particular techniques to reduce the amount of pivoting and communication between the hybrid components. This results in an efficient algorithm with balanced use of a multicore processor and a graphics processor.